Let G be a compact Lie group acting on a closed manifold M.
Partially motivated by work of Uhlenbeck (1976), we explore the
generic properties of Laplace eigenfunctions associated to
G-invariant metrics on M. We find that, in the case where 𝕋 is
a...
What happens to an Lp function when one truncates its Fourier
transform to a domain? This question is now rather well understood,
thanks to famous results by Marcel Riesz and Charles Fefferman, and
the answer depends on the domain: if it is a...
Interaction models discussed here are the (asymmetric) quantum
Rabi model (QRM), which describes the interaction between a photon
and two-level atoms, and the non-commutative harmonic oscillator
(NCHO). The latter can be considered as a covering...
In spite of tremendous progress in the mean-field theory of spin
glasses in the last forty years, culminating in Giorgio Parisi’s
Nobel Prize in 2021, the more “realistic” short-range spin glass
models have remained almost completely intractable. In...
In the search for possible blow-up of the incompressible
Navier-Stokes equations, there has been much recent attention on
the class of axisymmetric solutions with swirl. Several interesting
structures of this system have led to regularity criteria...
In 1982, S. T. Yau conjectured that there exists at least four
embedded minimal 2-spheres in the 3-sphere with an arbitrary
metric. In this talk, we will show that this conjecture holds true
for bumpy metrics and metrics with positive Ricci...
I will describe the construction of a harmonic measure that
reproduces a harmonic function from its Robin boundary data, which
is a combination of the value of the function and its normal
derivative. I shall discuss the surprising fact that this...
An interesting feature of General Relativity is the presence of
singularities which can occur in even the simplest examples such as
the Schwarzschild spacetime. However, in this case the singularity
is cloaked behind the event horizon of the black...
We consider 2D quantum materials (non-magnetic and constant
magnetic field cases), modeled by a continuum Schroedinger
operator, whose potential is a sum of translates of an atomic well,
centered on the vertices of a discrete subset of the plane...
This talk is a discussion about the extremal points of the unit
ball with respect to the Hessian-Schatten variation seminorm, i.e.
the total variation of the second distributional differential with
respect to the Schatten matrix norm. The main...
